A reproducing system is a countable collection of functions {φj : j ∈ J } such that a general function f can be decomposed as f = ∑ j∈J cj(f) φj , with some control on the analyzing coefficients cj(f). Several such systems have been introduced very successfully in mathematics and its applications. We present a unified viewpoint to the study of reproducing systems on locally compact abelian grou...

The dicistrovirus intergenic internal ribosome entry site (IGR IRES) directly recruits the ribosome and initiates translation using a non-AUG codon. A subset of IGR IRESs initiates translation in either of two overlapping open reading frames (ORFs), resulting in expression of the 0 frame viral structural polyprotein and an overlapping +1 frame ORFx. A U-G base pair adjacent to the anticodon-lik...

We study singly-generated wavelet systems on R that are naturally associated with rank-one wavelet systems on the Heisenberg group N . We prove a necessary condition on the generator in order that any such system be a Parseval frame. Given a suitable subset I of the dual of N , we give an explicit construction for Parseval frame wavelets that are associated with I . We say that g ∈ L(I×R) is Ga...

A reference frame F is described by the element g of the Poincaré group P which connects F with a given fixed frame F 0. If F is a quantum frame, defined by a physical object following the laws of quantum physics, the parameters of g have to be considered as quantum observables. However, these observables are not compatible and some of them, namely the coordinates of the origin of F , cannot be...

The main scope of this paper is to examine the smoke ring (or vortex filament) equation which can be viewed as a dynamical system on space curve in E³. differential geometric properties soliton surface accociated with Nonlinear Schrödinger (NLS) equation, called NLS or Hasimoto surface, are investigated by using Darboux frame. Moreover, Gaussian and mean curvature found terms curvatures k_{n}, ...

In this paper, we introduced and characterized the controlled $g$-duals of a frame in separable Hilbert space $\mathcal{H}$ . Afterwards, obtained new $C$-controlled $g$-dual frames from given frames. addition, approximation for was defined some their properties were investigated. Finally, relationship between approximately dual $g$-dual.

This work develops a quantitative framework for describing the overcompleteness of a large class of frames. A previous article introduced notions of localization and approximation between two frames F = {fi}i∈I and E = {ej}j∈G (G a discrete abelian group), relating the decay of the expansion of the elements of F in terms of the elements of E via a map a : I → G. This article shows that those ab...

Frames for Hilbert spaces were first introduced by Duffin and Schaeffer [10] in 1952 to study some problems in nonharmonic Fourier series, reintroduced in 1986 by Daubechies, Grossmann and Meyer [8]. Frames are very useful in characterization of function spaces and other fields of applications such as filter bank theory, sigmadelta quantization, signal and image processing and wireless communic...

This paper studies the problem of sequence-to-sequence alignment, namely establishing correspondences in time and in space between two di erent video sequences of the same dynamic scene. The sequences are recorded by uncalibrated video cameras, which are either stationary or jointly moving, with xed (but unknown) internal parameters and relative inter-camera external parameters. Temporal variat...